On Huygens’ principle and perturbed elastic waves

Abstract

We consider smooth solutions of a perturbed system of linear elasticity in 3-D and concentrate our attention on the following question: Is it possible that all such perturbed elastic waves propagate on spherical shells? We prove that the answer is negative for a suitable class of perturbations. The main technical difficulties in proving our results arise from the fact that in elasticity there are two waves, the longitudinal and the transverse wave, which propagate at different phase velocities. Our analysis is based on estimates over characteristics cones and a "trace type" theorem suitably adapted for our needs. © 1992, Khayyam Publishing. All rights reserved.

Publication Title

Differential and Integral Equations

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